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Developments in Maritime Transportation and Exploitation of Sea Resources Guedes Soares & Lpez Pea (eds)

2014 Taylor & Francis Group, London, ISBN 978-1-138-00124-4

Numerical simulation of steady and unsteady current velocity of a vertical axis marine turbine

I. AminDepartment of Naval Architecture and Marine Engineering (NAME), Faculty of Engineering, Port Said University, Port Said, Egypt

Q. XiaoDepartment of Naval Architecture and Marine Engineering, Strathclyde University, Glasgow, UK

ABSTRACT: Motivated by the importance of investigating the hydrodynamic performance of Verti-cal Axis Marine Current Turbine (VAMCT) in field like to real marine environment, this work presents numerical simulation of VAMCT in both steady and unsteady current velocity. Three bladed turbine is examined in order to evaluate the performance of VAMCT in fluctuating current velocity. Turbine model is studied using a time-accurate Reynolds-Averaged Navier-Stokes (RANS). Transient rotor-stator model with sliding mesh technique was used. User-Definition Function (UDF) is created to simulate random fluctuated current velocity. The results show that, there are significant decrease in power efficiency in unsteady current compared with steady case.

blades allowed to obtain the maximum power coef-ficient at small angular velocities. Another work for Castelli (Castelli, et al., 2012), investigates the optimal grid spacing and turbulence model for 2D numerical analysis of a vertical axis water turbine operating at a 2 m/sec free stream current velocity. Castelli concluded that, the resulting optimal mesh has appeared to be quite similar to that obtained for numerical analysis of vertical axis wind turbine. Marine current is accumulative consequence of ocean local and remote factors, such as winds, buoy-ancy fluxes, tides, and various types of waves. The influence of forces from above factors on marine current is not trivial. Many existing research works simply assume the current velocity as a fixed uni-form flow. However, the real marine current include internal waves, which formed from the interfaces of water layers and difference in density and tempera-tures in layers. These waves make marine current velocity becomes a fluctuating velocity form.

Generally, most measurements of marine cur-rent have focused on obtaining time averaged cur-rent speed. Little is therefore know about temporal fluctuations of marine current at the time scale of a few minutes and below, (Teigen, 2002). Two main types of marine current fluctuations can be identified based on the literature. At a large time scale, the marine current speed fluctuates with a period of 6 or 12 hours which is related to tidal astronomical phenomena. At a small time scale, it can fluctuate with a period of few seconds or less.

1 INTRODUCTION

Tidal turbine is one of the hydro-kinetic devices, which can be classified further as Horizontal Axis Marine Current Turbines (HAMCT) and Verti-cal Axis Marine Current Turbines (VAMCT), depending on the direction of rotational axis rela-tive to the water current flow direction. The major advantage of VAMCT is that it is able to extract hydrodynamic energy from any direction without adjustment or yawing system. Straight, untwisted and uniform section blades are simple to fabricate, and thus widely used for VAMCT. One commonly used tidal turbine is the Darrieus rotor, originally patented as wind turbine in the USA in 1931 by G.J.M. Darrieus, (Castelli, et al., 2012).

Investigation on the Vertical Axis Marine Cur-rent Turbine has been previously carried out from different points of view. Study of VAMCT from flow control strategy associated with swell effect was performed by Seif Elghali et al., (2010). Maitre, et al., (2012) investigated a Darrieus cross flow marine turbine with a two-dimensional RANS code. The influence of the near wall grid density on the numerical results was discussed. Castelli, et al. (2012) studied the flow characteristics for a three/four/five-blade Darrieus turbine at different tip speed and solidity ratios. The study has focused on the reduction of local blade torque variation by increasing the number of blades. Their results showed that, the turbine which has large number of

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An example of the power produced by a marine current turbine within 24 hours period is given by Zhou et al. (2012). Teign, (2002), studied the fluctuation of output electricity which generated from VAMCT at small time scale. He used com-puter program based on Fourier transforms with randomly selected amplitudes to measurement the electricity fluctuation, as shown in Figure 1.

Kang et al., (2012), measured instantaneous water velocity using an Acoustic Doppler Cur-rent Profiler (ADCP) over a 10 min period dur-ing a flood tide. The velocity measurements were performed under two different flow conditions (U = 1.53 and 2.01 m/s), and the time history of the instantaneous velocity was plotted by Kang, as shown in Figure 2. The study assumed that inlet velocity is uniform and did not take into account oncoming turbulence.

From the above literature review, it can be seen that the simulation of hydrodynamic performance of VAMCT under the condition of a fluctuated current velocity is neglected in most available publications. In the present work, a numerical simulation is car-ried out for a three straight bladed Darrieus VAMCT in steady and unsteady current velocity. The main

Figure 1. Time series of fluctuating current field, [2].

Figure 2. The time history of the instantaneous flow velocity measured upstream in the East River, [1].

objective is to model a VAMCT under a condition similar to real marine environment and evaluate its performance in unsteady current velocity.

2 NUMERICAL MODEL

Three bladed turbines is numerically solved by com-mercial code ANSYS 14 aiming to evaluate the per-formance of turbine in both steady and unsteady current velocity. Gambit software was used in mod-eling the domain and meshing the turbine.

2.1 Current fluctuation model

User Defined Function (UDF) is used to simu-late the current fluctuation in ANSYS software. Equation 1 is programmed with C++ Language and implemented in ANSYS software.

u t U AU f tii

n

( ) sin= + ( )=0 0

1

2 (1)

where, U0, is the initial steady current velocity, A is current amplitude, fi is fluctuating current fre-quency, and t is the time.

In case of steady current velocity, the current speed is selected to be equal to 2 m/sec as a initial steady current (4 knots), which is compatible with the technical and economical analysis which being suggested by Marine Current Turbines Limited, Fraenkel (2002).

Equation 1 presents Fourier expression which used to create random current velocity from three sinusoidal wave, which have different amplitudes and frequencies. The current amplitudes for the three sinusoidal wave are 0.2 m, 0.1 m and 0.05 m. The current frequencies are 100 rad/sec, 30 rad/sec and 5 rad/sec. According to this data, the maxi-mum current value is 2.35 m/sec and the mini-mum is 1.65 m/sec. The inlet velocity is fluctuated dependents to time flow as shown in Equation 1. the Equation results is shown in Figure 3 as a rela-tion between current velocity value and time flow.

2.2 Computational methodology

The key parameters which quantify the turbine performance include the power coefficient Cp, the blade moment coefficient Cm, the blade tip speed ratio and the blade lift coefficient CL. They are defined as follows

The blade lift coefficient

CL

U AL

s

=0 5 2. (2)

where L is the lift force.

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The power coefficient

CP

U Ap

s

=0 5 3. (3)

The total power

P Mii

= 2 (4)The blade moment coefficient

CM

U Am

s

=0 5 2. (5)

The turbine blade tip speed ratio

= RU

(6)

where P is the power generated by turbine defined in Equation (4), 2 is the turbine angular veloc-ity, Mi is the blade moment relative to the turbine center, is the fluid density, U is the velocity of the incoming flow, As is the turbine swept area and R is turbine radius.

The blade Reynolds number for this work was defined as:

RR c

e = ( ) (7)where c is the blade chord. The dynamic viscosity was assumed to be 0.0013 and the density was set to 1000 kg/m2. The Reynolds number in this study was varied from 6.35 104 to 1.922 105, from this range of Reynolds number, typical turbulence flow case was assumed.

The solidity parameter is defined as

= c NR

(8)

where N is the number of turbine blades.

Figure 3. Relationship between current velocity fre-quency and turbine rotation frequency.

Figure 4. Azimuthal coordinate of blade.

Table 1. Main geometrical features of the analyzed rotor.

Dimensions

Diameter Drotor [mm] 1030

Height Hrotor [mm] 1456.4

Number of blade N [-] 3Blade profile NACA 0021

Chord length c [mm] 85.8

Spoke-blade connection 0.25 c

Solidity parameter 0.5

2.3 Model geometry and computational domain

The main features of the turbine are summarized in Table 1. Rotor azimuthal position is identified by the angular coordinate of the blade center of blade No.1, which was settled at 0.25 c for NACA 0021 airfoil, as can be seen in Figure 4.

Straight blades with symmetric NACA 0021 airfoil are modeled. Neither supporting arms of blades nor shaft is included.

Figure 5 shows the dimensions and the bound-ary conditions of the computational domain. The computational domain width was set 20 time rotor diameters to avoid any interference between the rotor and the boundaries. In order to allow a full

Figure 5. Main dimension of the computational domain.

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development of the wake, inlet and outlet bound-ary conditions placed respectively 10 time upwind and 16 time downwind with respect to the center of rotor place. Two symmetry boundary condi-tions are used for the two side walls. The circumfer-ence around the circular opening, centered on the turbine rotational axis, is set as an interface, thus ensuring the continuity in the flow field. Unstruc-tured mesh was chosen for the domain with rotor, in order to reduce time to prepare the CFD simula-tions. Mesh around blades and rotor are shown in Figure 6. The inlet is set as a velocity inlet, with a constant current velocity of 2 m/sec in steady con-dition. while, was set as UDF file in fluctuated cur-rent condition. outlet was set as a pressure outlet.

3 RESULTS AND DISCUSSION

A numerical study is performed on a VAMCT in steady and unsteady marine current velocity, the study aimed to identify the performance of VAMCT in unsteady current velocity. In the follow-ing, we start with the description of the simulation set-up, followed by the validation and verification of developed numerical methods. The simulated results are presented in graphic diagrams show-ing the difference between the power coefficient performance in both steady and unsteady current velocities.

3.1 Simulation set-up and turbulence model selection

A transient rotor-stator model is employed to model the flow field around blade with unsteady

simulation. A moving mesh technique is applied to rotor turbine blades at a constant rotational speed.

Similar to wind turbine, the blade of marine tidal turbine varies its angle of attack during one rotating cycle. At a large angle of attack, dynamic stall phenomenon appears, causing large flow separation. Once it occurs, the choice of a proper turbulence model is very important in order to accurately predict the flow with large adverse pres-sure gradient and separation.

Ferreira et al. (2007) found that one-equation Spalart-Almaras model and two-equation k - models are unable to predict the large eddies at high angle of attack. Wolfe and Ohcs (1997) showed that Standard k - model may lead to inaccurate results when the flow separation occurs. Howell, et al. (2010) used RNG k - model and concluded that this model can predict flow field with large flow separations more accurately than Standard k - model. Yu, et al. (2010), showed that the choice of k - SST turbulence model can obtain good results because of its capability of capturing the main flow-field characteristics in the near wall layers and separated flow regions. Therefore, k - SST turbulence model is selected for the present work, according to Yu recommendation.

3.2 Verification

CFD mesh dependence test implies to perform a series of calculations with different grids by vary-ing number of nodes and elements, for evaluat-ing convergence of most relevant flow variables, which in this case is the torque transferred from fluid to blades. Three different grid node densi-ties are examined: coarse (about 64,000), medium (about 128,000), and fine (about 276,000). Details of grid information are included in Table 2. Three different start size meshes were presented with the same growth rate equal to 1.05. Grid size limit are changed from 0.25 in case of fine mesh to 0.65 in case of coarse mesh density. Start grid size are var-ied from 0.01 in case of course mesh to 0.006 in case of fine mesh. Results of validation in three dif-ferent grids for the average power coefficient are: coarse, 0.358; medium, 0.323; and fine, 0.319 along

Figure 6. Mesh around turbine rotor and airfoil NACA 0012.

Table 2. Grid dependence test (Errors are estimated based on experimental Cp = 0.31).Mesh density Growth %

No. of mesh elements Cp Error

Coarse 1.05 64,000 0.358 18.7%

Medium 1.05 128,000 0.323 4.2%

Fine 1.05 276,000 0.319 2.9%

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a complete revolution of blades at (TSR = 3.0). The error was calculated as a percentage based on experimental Cp value which is equal to 0.31 (according to Castelli, et al. (2012)). The running time is calculated for the three cases, the running time of fine mesh expended about 12 hour from each run. while, in case of medium and course mesh expended about 5 and 3 hours respectively. A grid that represents a compromise between the accuracy and computational cost is selected. The total Cm of 3 bladed turbine obtained for three sets of grids, then the total power coefficient, Cp is calculated and plotted in Figure 5. Based on the comparison in Figure 5 and the calculated error percentage in Table 2, there is no significant difference between the plotted curve and error percentage in case of medium and fine grid, therefore for simplicity pur-poses and time saving, all simulations in this work are computed by using a medium grid.

3.3 Validation

In order to validate our numerical model devel-oped, simulation is conducted with a steady cur-rent velocity. The results of power coefficient at different tip speed ratios are compared with experi-mental results of Castelli, et al. (2012), as shown in Figure 6. The validation process done in range of tip speed ratio from 1.44 to 3.09, based on the available data from Castelli, et al. (2012). The com-putational result shows good agreement as com-pared with Castellis experimental result especially at high TSR range. The high discrepancy between numerical and experimental results at lower TSR

Figure 5. Power coefficient of modeled VAMCT dur-ing one revolution for different meshing size under steady current velocity condition.

Figure 6. Comparison of power coefficient variation with TSR for numerical and experimental data, which presented in Castelli, et al. (2012).

Figure 7. The torque of the three blades of 3-blade VAMCT (steady condition, TSR = 3).

can improved in future by increase the meshing around blades.

3.4 The performance of vamct under steady and unsteady current velocity

Three bladed turbines is numerically solved aiming to evaluate the performance of turbine in both steady and unsteady current velocity. Two current velocities models are assumed in this study and setup as veloc-ity inlet, one is fixed value 2 m/sec (steady case) and the other is fluctuated (unsteady case).

The two cases were numerically solved and the results were graphically plotted from Figures 7 to10. The torque results of the turbine under steady

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condition at TSR = 3.0 is shown in Figure 7. While, the torque of the same turbine under unsteady cur-rent velocity is shown in Figure 8. It can be seen in Figure 7 the symmetrical cycle performance which is known for this type of turbines. The symmetri-cal trend is disappear in unsteady case, as shown in Figure 8, but the three cycle is clearly shown dur-ing the revolution.

Power coefficient is calculated and plotted for both steady and unsteady cases, as shown in Figure 9. The comparison shown in Figure 9 shows that there are three local increment in power coef-ficient for the three blades cycles. But the total area under power coefficient curve in unsteady case is little small that steady case.

The power performance of the turbine in both steady and unsteady current velocity is plotted at different TSR, as shown in Figure 10. The figure shows that there is significant decrease in power in unsteady case compared with steady one, espe-cially at high TSR (TSR > 2.0). While at small TSR (TSR >2.0) there are no differences in perform-ance between steady and unsteady cases.

4 CONCLUSION

Three bladed turbine is numerically analyzed in steady and unsteady marine current velocity in order to evaluate performance of this turbine in both cases. Fluctuating current velocity is modeled and presented in Fourier expression. The mod-eled Fourier expression results like to real marine current fluctuation which was measured in tidal region. The presented turbine model is design and solved numerically. The meshed is verified and the grid tested at different meshing and nodes num-bers. Computational predictions of the power coefficient of the turbine carried out and validated with available experimental data.

The results of steady and unsteady cases show that, there are significant differences between two cases and the assumption of steady case could be not suitable in design stages. The total power coefficient of unsteady case is decreased with about 7.5% com-pared with steady case at TSR = 3.0. While there are no change in power coefficient at small TSR. Also, there are significant increase in local torque humps and hollows in unsteady case, which should be con-sidered in structure analysis of such turbines.

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Figure 8. The torque of the three blades of 3-blade VAMCT (unsteady condition, TSR = 3).

Figure 9. Comparison between the power coefficient in both steady and unsteady cases at TSR = 3.

Figure 10. Comparison between the power coefficient in both steady and unsteady cases at different TSR.

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